Multiscale mushy layer model for Arctic marginal ice zone dynamics.

Perhaps the most dynamic component of the Arctic sea ice cover is the marginal ice zone (MIZ), the transitional region between dense pack ice to the north and open ocean to the south. It widens by a factor of four while seasonally migrating more than 1600 km poleward in the Bering-Chukchi Sea sector, impacting climate dynamics, ecological processes, and human accessibility to the Arctic. Here we showcase a transformative mathematical modeling approach to understanding changes in MIZ location and width, focusing on their seasonal cycles as observed by satellites.

Uncertainty quantification for ecological models with random parameters.

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters.

Percolation analysis for estimating the maximum size of particles passing through nanosphere membranes.

Percolation theory can be used to study the flow-related properties of various porous systems. In particular, recently developed membranes from silica nanoparticles with surface grafted polymer brushes represent a quintessential hard-sphere soft-shell system for which fluid-flow behavior can be illuminated via a percolation framework. However, a critical parameter in membrane design involves the maximum pass-through size of particles.

Anderson Transition for Classical Transport in Composite Materials.

The Anderson transition in solids and optics is a wave phenomenon where disorder induces localization of the wave functions. We find here that the hallmarks of the Anderson transition are exhibited by classical transport at a percolation threshold-without wave interference or scattering effects. As long range order or connectedness develops, the eigenvalue statistics of a key random matrix governing transport cross over toward universal statistics of the Gaussian orthogonal ensemble, and the field eigenvectors delocalize.

Spectral analysis and connectivity of porous microstructures in bone.

Cancellous bone is a porous composite of calcified tissue interspersed with soft marrow. Sea ice is also a porous composite, consisting of pure ice with brine, air, and salt inclusions. Interestingly, the microstructures of bone and sea ice exhibit notable similarities.